On 2 twisted pairs of the internal cables I have a cable tv set up which needs 50Mbps for 4K video so 2 twisted pairs will be dedicated to the cable tv. The other 2 twisted pairs I would like to set up as a separate LAN and phone line.
That won't work – you don't have enough spare pairs for that. With a 4-pair cable you can have either two LANs, or one LAN + landline, but can't fit all three.
Each standard 10/100 Mbps Ethernet connection requires two pairs. If you had two such connections on the cable, you wouldn't have any pairs left for the telephone – yes, you can share a Cat5 cable between Ethernet and analog telephone (and that was where Ethernet's usage of Cat5 comes from in the first place), but not both on the same wires.
(If I understand it correctly, the fact that standard Ethernet is a "baseband" signal – the 'BASE' in 100BASE-TX – means it would conflict with analog telephone on the same wires, as opposed to something like ADSL which uses a "broadband" signal that's modulated on a higher frequency.)
I think your options are:
One 10/100 Mbps connection + landline + one unused pair.
If the TV requires 50 Mbps, that still leaves you with another 50 Mbps – it would be possible to use a pair of managed Ethernet switches to isolate two logical VLANs over the same physical connection, and even to set up QoS so that the TV would have a guaranteed 50 Mbps capacity no matter what the other VLAN is doing.
All four pairs for a 1 Gbps Ethernet connection, no analog landline.
From what I've heard, a pair of old Cisco ATA devices could be used to transform an analog line into VoIP on one end, then back to analog on the other.
If you can find that kind of equipment, then a 1 Gbps Ethernet connection would give you plenty of capacity for the TV VLAN and your general-purpose VLAN and the VoIP VLAN all at once.
One standard 10/100 Mbps Ethernet connection on two pairs + landline + one 100BASE-T1 Ethernet connection on the remaining pair. The latter is a fairly new standard, and it's meant for industrial and automotive Ethernet connections rather than general home use, so it would probably be difficult to find equipment for it – but it's technically a possibility.
One 1 Gbps or two 10/100 Mbps Ethernet connections over the cable, and some kind of wireless setup for the landline. I don't know much about this area, but I think I've seen DECT equipment that would make it possible?
One 10/100 Mbps Ethernet for the TV + one landline, and wireless LAN from the existing APs – e.g. one of those 'mesh' systems or an 'extender' that lets you connect wired Ethernet equipment to it.
MoCA, if the building happens to have coax for cable TV.
Power line networking, as mentioned in comments – but in my experience it highly depends on the building and its electric wiring, as I've tried several kinds of HomePlug AV in the past and could never get it to reach even a third of its advertised speed nor stability.
The cable has been set up as a single sequential path, i.e. in the first AP, I see one cable wired up, in each of the other APs I see 2 cables, one coming in from last AP and then one out to next AP. And then finally I see the last AP with just the incoming AP wired up.
That works, but really isn't a nice way to do things... both in terms of reliability and performance. (And requiring APs that have two Ethernet ports, too – many only have one – or an extra switch next to each AP.)
Hopefully at least the APs are all in bridge mode (i.e. actual APs and not whole routers).